“My letter to the Examiners, announcing my intention of sitting for Fellowship (which like all other such documents is preserved on my quires) was delivered on Sept 21st.  The Examination took place on Sept. 22nd and the two following days.  On Oct. 1st, 1824, at the usual hour of the morning, I was elected Fellow.  There were elected at the same time T.B.  Macaulay (afterwards Lord Macaulay), who was a year senior to me in College, and I think Field of my own year.  I drew up my letter of acknowledgment to the Electors.  On Oct. 2nd at 9 in the morning I was admitted Fellow with the usual ceremonies, and at 10 I called on the Electors with my letter of acknowledgment.  I immediately journeyed to Derbyshire, paid a visit at Edensor, and returned by Sheffield.

“On Oct. 11th (it having been understood with Mr Higman that my engagement as Assistant Mathematical Tutor stood) the Master sent for me to appoint me and to say what was expected as duty of the office.  He held out to me the prospect of ultimately succeeding to the Tutorship, and I told him that I hoped to be out of College before that time.

“About this time the ‘Athenaeum,’ a club of a scientific character, was established in London, and I was nominated on it, but I declined” (Oct. 14th).  In this year (1824) I commenced account with a banker by placing L110 in the hands of Messrs Mortlock and Co.  On Oct. 16th I walked to Bury, and after a single day’s stay there returned to Cambridge.

“On Oct. 23rd, 1824,1 began my lectures as Mathematical Assistant Tutor.  I lectured the Senior Sophs and Junior Sophs on Higman’s side.  The number of Senior Sophs was 21.  Besides this I took part in the ‘Examinations of the Questionists,’ a series of exercises for those who were to take the Bachelor’s degree in the next January.  I examined in Mechanics, Newton, and Optics.  I had also as private pupils Turner, Dobbs, and Cooper.  I now ceased from the exercise which I had followed with such regularity for five years, namely that of daily writing Latin.  In its stead I engaged a French Master (Goussel) with whom I studied French with reasonable assiduity for the three terms to June, 1825.

“Among mathematical investigations I find:  Theory of the Moon’s brightness, Motion of a body in an ellipse round two centres of force, Various differential equations, Numerical computation of sin pi from series, Numerical computation of sines of various arcs to 18 decimals, Curvature of surfaces in various directions, Generating functions, Problem of sound.  I began in the winter a Latin Essay as competing for the Middle Bachelors’ Prize, but did not proceed with it.  I afterwards wished that I had followed it up:  but my time was fully occupied.

“On Jan. 28th, 1825, I started for Edensor, where I paid a visit, and returned on Feb. 2nd.  On Feb. 4th I wrote to Mr Clarkson, asking his advice about a profession or mode of life (the cares of life were now beginning to press me heavily, and continued to do so for several years).  He replied very kindly, but his answer amounted to nothing.  About the same time I had some conversation of the same kind with Mr Peacock, which was equally fruitless.